Laplace question

Question

How do you express Laplace transform $\mathcal{L}(g)(z)=\int_{0}^\infty e^{-zt}g(t)dt$ with Fourier transform? And how do you form the reverse formula for Laplace transform using Laplace transform value $\mathcal{L}(g)(\sigma + \mathbf{i}y)$, $y\in \Bbb{R}$. We can assume the functions are integrable.

Answer 1

laplace transform introduce variable $s$ as $s=\sigma+j*\omega$,

if $\sigma=0$ then lapalce transform is same as fourier transform,which means that laplace transform only on imaginary part is equivalent to fourier transform